# How do you write # (2x^2 - 5x + 4) ^2 in standard form?

May 18, 2017

$4 {x}^{4} - 20 {x}^{3} - 41 {x}^{2} - 40 x + 16$

#### Explanation:

$\textcolor{b l u e}{\left(2 {x}^{2} - 5 x + 4\right)} \textcolor{g r e e n}{\left(2 {x}^{2} - 5 x + 4\right)}$

Multiply everything inside the right bracket by everything in the left.

$\textcolor{b l u e}{\textcolor{w h i t e}{-} 2 {x}^{2}} \textcolor{g r e e n}{\left(2 {x}^{2} - 5 x + 4\right)} \to 4 {x}^{4} - 10 {x}^{3} + 8 {x}^{2}$
$\textcolor{w h i t e}{.} \textcolor{b l u e}{- 5 x} \textcolor{g r e e n}{\left(2 {x}^{2} - 5 x + 4\right)} \to \text{ } - 10 {x}^{3} + 25 {x}^{2} - 20 x$
$\textcolor{w h i t e}{. .} \textcolor{b l u e}{+ 4} \textcolor{g r e e n}{\left(2 {x}^{2} - 5 x + 4\right)} \to \underline{\text{ } + 8 {x}^{2} - 20 x + 16}$
$\text{ } 4 {x}^{4} - 20 {x}^{3} - 41 {x}^{2} - 40 x + 16$